qui

knew

that

And I had the impression after the discussion that I may have

confused some of you by switching back and forth between the

photon concept to explain these forces and this classical

oscillator model.

And so some people are asking whether one of these forces is

somehow derived in one of the models and the other one is

solved. And I just want to clarify that you can use either

the photon concept or this classical model to derive both

forces. So both the scattering force as well as the optical

force can be derived in both pictures and you can get

identical results. But what you get are mean forces.

If you look at the fluctuations you somehow have to either do

the quantum electric variation and the quantum fluctuation

that I do this or in this classical model you have to

consider that the fields you are interacting with have

fluctuations on a certain level and the atomic dipole also

has quantum fluctuations. And if you kind of put this in by

hand in this classical model you also get fluctuations of the

photon.

Just to make a brief illustration again how these two

forces arise in the photon picture. So as I mentioned the

scattering forces due to absorption and spontaneous emission.

So imagine you have a single laser beam that hits the atom

and interacts with the atom say with a certain detuning.

Then you can absorb a photon from the incoming laser that's

the absorption and then you do spontaneous emission and

spontaneous emission sends out a photon but the direction of

this spontaneous emission is random. So in each single scattering

event you have a momentum kick from both absorption and

spontaneous emission. But if you average over many such cycles

then the contribution from the spontaneous emission which

goes in random direction averages while the contribution

from the absorption adds up. So you get a mini scattering

force which is always pointing along the direction of the

laser and that is called the scattering force. And you can

also see it's always repulsive so you will never have an

attractive scattering force in a sense. The laser always

repels the atoms and pushes them in the direction of laser

properties. The dipole force on the other hand is due to

absorption and stimulated emission. And to get the dipole

force you actually need at least two k vectors in your laser.

If you just have a single laser, a single plane wave of

electromagnetic field you won't have a dipole force, a

mean dipole force because absorption and stimulated

emission will always go into the same mode and the net

momentum transfer is zero. So you need at least an

intensity gradient which means you focus your beam. But